Management instrument



Dec. 8, 1942. H. WALLER ETAL I 2,304.132

MANAGEMENT INSTRUMENT F iled Sept. 15, 1941 5 sheets-$118 1 1 1 ENTORS#528527" M/SQLEIQ 14L FEED F. 861%! OMAN/v kellu, 5',

ATTORNEY Dec. 8, 1942. H. WALLERET AL 2,304,132

' MANAGEMENT INSTRUMENT A Filed sept. 15, 194; 5 Sheets-Sheet 2 V v V F.5.

r 19 I I I I I I I T I/ Q JB, 5

BY M274 QM Ky.

A 7'7'ORNEY Dec. 8, 1942. H. WALL-ER ETAL 2,304,

MANAGEMENT INSTRUMENT 'Filed Sept. 1:5, 1941 5 sheets-sheet 5IIIIIIIIIJ:

F J INVENTORS HERBERT 14444152 BY -/)4 FR0 F. SCHL OMAN/V ATTORNEY Dec.8, 1942. H WALLER ETA]. 2,304,132

MANAGEMENT INSTRUMENT Filed Sept. 15, 1941 5 Sheets-Sheet 4 "Hm-- o o AT TOR/V5 Y Bed. 8, 1942. H. WALLER ETAL 2,304,132

MANAGEMENT INSTRUMENT Filed Sept. 13, 1941 5 Shaets-Shet 5 INVENTORS ATTORNEY- aiented ee. 8, W42

spree Fwd asserts transom/mar ras'rnmrnn'r Herbert Waller and .ilired F.Schlomann,

- New York, N. Y.

20 Claims. (or. se -e7) The present invention relates to an instru= mentfor use in the analysis and in the manage ment of business enterprises.Ihe object of the invention is the provision of an instrument wherebycertain data essential to the conduct of a business may be ascertainedin a particularly simple manner and without the requirement of applyingcumbersome mathematical calculations. The invention consists of aninstrument comprising several rulers adjustable relatively to each otherand to the scale-provided axes of a coordinate system whereby the rulersadjusted to certain data will indicate the data to be ascertained.

Further objects and details of the invention will be apparent from thedescription given here inafter and the accompanying drawingsillustrating an embodiment thereof by way of (EX-Y ample. In thedrawings:

Figs. 1 to 5 are diagrams illustrating the principle underlying theinvention.

Fig. 6 is a top plan view of an instrument according to the invention inits preferred form.

Fig. 7 is a side elevation thereof.

Fig. 8 is a cross-section along line 8-8 of Figs '7.

Fig. 9 is a bottom plan view of a portion of the instrument on a largerscale.

Fig. 10 is a cross-section along line iii-4t of Fig. 9.

Fig, 11 is a bottom plan view of another portion of the instrument.

Fig. 12 is a section along line i2l? of Fig. 11.

Fig. 13 is a section along line i3-l3 of Fig. 11.

Fig. 14 is a section along line 3-46 of Fig. 6.

Fig. 15 is a section along line i5-i5 of Fig. ti, and

Fig. 16 is a diagram illustrating the application of the instrument fora specified purpose.

In the diagram of Fig. l a rectangular co-ordinate system is shown withthe positive leg of the m-axis intersecting the y-axis in the zero point0 and thereby determining the positive leg +11 and the negative leg -y.Each of the axes is provided with a scale only part of which is in-.dicated and the length of the increment of the scale of the m-axis isdenoted by a and that of the y-axis by b. The scale of the :c-axis isused to indicate volume of production or sales, and that of the y-axisto indicate costs and profit or loss.

portion to the sales.

ness for which the diagram is made. In consid= ering this relation, itmay be assumed that the variable costs increase and decrease in directpro Should this assumption be incorrect in a particular case, it will beeasy to make the diagram correspond to the facts. However, we have foundthat cases requiring such adaptation are exceptional and, for thatreason, will not require special attention in the subsequentexplanation. Moreover, the users of instruments according to theinvention can be assumed to have suincient knowledge and experience inbusiness accounting so that they will not encounter any difiiculties inmaking proper use of the instrument in the rare cases where deviationsfrom the afore-mentioned proportionality are large enough to deserveconsideration.

The diagram according to Fig. l. is so prepared that all costs andlosses appear in the +3. s! quadrant, i. (-2., below the m-axis of theco-ordinate system; whereas profits are shown in the +2:, +11 quadrant,i. e.,'above the :r-axis. Now, in

i order to explain the diagram, let it be assumed Y plotted; FA beingparallel to the :a-axis.

that in the business under consideration the total sales equal to 3dollars were made in a cer-= tain period and that these sales requiredthe expenditure of dollars in fixed costs and 1: dollars in variablecosts; hence, the profit is r=s --(f+vl Ii f+o is greater than 8, 1 willhave a negative sign indicating loss rather than profit. By setting oilthe value of s in scale measure of the :r-axis along the latter from thepoint 0, the

point T is determined. Point F is found by se-t= ting on on the g legthe value in the scale measure of the y-axis so that OF=; and shah larly'I'W is made equal to f+o.' Upward of point T line WT is extended topoint P so selected that PT=r. Then, the lines FW, FI? and Fe are.i.ccording to the construction of this diagram, TA= AW=21 and b PW -OTwherein is the ratio of the increment of the scale oi y-axis over thatof the scale of the Hence, with a axia.

we find cree er.

. over total sales.

' Line FP is termed the result line of the business under consideration;it is characterized by the fact that the ordinate of any point of thatline equals the profit or loss of the business to be obtained from salescorresponding to the abscissa of said point, for instance, sales OT willresult in a profit PT, and sales OT will resultin a loss P'T'. The pointof intersection 3B of the result line F'Pwith them-axis is the so-calledbreak-even point indicating that volume of sales which is equal to thesum of the fixed and variable costs appertaining to such sales. Thissales volume will be referred to hereinafter as the break-even volume.It will be clear that any volume of sales in excess of the break-evenvolume will result in a profit, whereas a sales volume of less than theamount OB will result in a loss. Hence, if the fixed and variable costsappertaining to a certain sales volume are known, the entire diagram canbe plotted showing the break-even point and volume, the total costs, thevariable costs, and the profit or loss resulting from any othercontemplated sales volume.

In addition to the knowledge of the relation of sales, fixed andvariable costs, and profit or loss, there are of particular interest inthe analysis and management of a business three ratios which we havetermed the specific yield, the margin of profit, and the determinant.The specific yield is defined as the profit or loss resulting from aparticular sales volume over the difference between such sales volumeand the break-even volume. The margin of profit is the profit or lossThe determinant is the amount the sales are in excess or fall short ofthe breakeven volume over the total sales.

In order to find the specific yield Y in the diagram of Fig. l, theconditions prevailing in connection with the sales volume 3 may beselected as an examp e. The sales s correspond to the distance OT, theprofit is represented by thedistance PT and the difference between thesales volume s and the break-even volume is its zero mark and its 100mark respectively coincide with the litres FF and FW, then line FA willdirectly indicate at Y1 on the scale of the ruler the specific yield inper cent. The correctness of this statement follows from the similarityof the triangle PWF and the triangle having Z as its base and point F asapex. A slide or ruler Z would be equal to the fixed costs. The specificrepresented by the distance BT. However, in

order tofind the specific yield determined by these conditions it mustbe consideredthat in the present example the scales of the ordinates andabscissae of the system differ from each other. Therefore, thespecificyield must be written as zPT W wherein ePT ePA PA ET A or Consideringfurther that the volume of the total sales is equal to the sum ofvariable costs plus may write 0T=zPW.

Gonsequently, we find that the specific yield is represented by theratio' of the length P1. to the length PW. In order to measure thisratio. a

vertical slide or ruler Z of any desired prede position Zy where it isparallel to the y-axis, and

yield becomes zero when the break-even point is in the infinity. Inthat-case line FP coincides with FA, and therewill be a loss equal tothe amount of the fixed costs no matter what sales volume is reached. Ifthe specific yield becomes negative then the break-even point will also.be negative and the loss will always be greater than the fixed cost. Insuch a case the break-even point would not appear in an instrument whichprovides only for the positive leg of the :r-axis. Nevertheless, thepertaining specific yield can be found in the +x, y quadrant of thesystem. This is shown in the diagram of Fig. 2. In this diagram for asales volume corresponding to CT: the fixed costs are represented by thelength OF: or TzAz, the variable costs by AzWz and the loss by TzPz.Hence, the break-even point is at B2, and the specific yield isConsidering the similar triangles B2T2P2 and F2A2P2, we find Owing tothe construction of the diagram,

FzA2=OT2=Z(T2W2'-T2P 2) =Z.P2W2

Hence,

Then, the slide Z may be applied between the lines F'zAz and F'zW'z inthe position Z'y, whereupon line F2P2 will indicate the specific yieldon the scale of the slide at Ya. From the foregoing it will be clearthat the lower limit of the specific yieldis -1. This value will beattained when the line FzPz coincides with the line F2W2. Thus, thespecific yield can be found and measured within its entire range between+1 and --1.

In a similar manner the margin of profit can be found in the diagram ofFig. 1. According to its definition, as the ratio of profit or loss overthe total sales, its value M is Since, however, OT=z.PW,

values zero and 1, for instance for the sales volume T in the diagram ofFig. 1, the point P2 is determined so that PP2=T'P. Then the line FPzwill intersect; the slide in the position Zy at the desired point M2 ofthe slide scale to be read with a negative sign. The correctness of thisstatement can be proven as follows: According to the definition themargin of profit for the sales volume T is This ratio is indicated at Maowing to the similarity of the triangle FP'W having its apex at F and,its base in the slide Zy. The values of the margin of profit below 1 canbe measured in a somewhat modified method. Since, however, these valuesdo not frequently occur the explanation of such modified method appearsto be superfluous.

The determinant, finally, is the ratio of the sales in excess of thebreak-even volume over total sales or the ratio of the amount by whichand the triangle.

Therefore, the determinant for the point T? can be written as and isindicated at D2 by the extension of line FPz on the slide scale in theposition Zd.

A'particular feature of the diagram hereinbefore discussed is the fixedrelation of the length of the abscissa of any sales volume to the sum ofthe ordinate lengths for fixed costs, variable costs and profit or losswhich appertain to such sales volume. This permits construction of thediagram and reading of the three characteristic ratios, viz, Y, M and Din a simplified manner illustrated in the diagram of Fig, 3 in which thea: and y axes, the result line and total cost line are shown inpositions similar to Fig. 1.

It has been stated hereinbefore that owing to the construction of thediagram, 0T=z.PW. This equation is valid no matter how the amount of thefixed and/or the variable costs vary for a given turnover. If {AFW isdenoted by a and ):PFA by 3 then A W PA 7 tan a+tan B-- Considering thatOT A W PA PW= T andFA=OT we find Hence, thesum of the tangents of theangles a and p is dependent only on the ratio of the increments of thescales on the x-axis and the y-axis.

Now, in view of this equation the result line FF and the total cost-lineFW can be reprethe sales fall short of the break-even volume over totalsales. Its limits are also +1 and within the range of positivebreak-even points A positive determinant can be found in the followingmanner: Considering the sales volume T,

the determinant Considering further the triangles PET and PFA,

PT I =H Therefore, by placing the slide Z in the position ,Zd where itsends coincide with the lines FP is to be found for the point T, we haveI D Ti T'B OT F A Owing to the similarity of the triangles PT'B andP'A'F,

According to the foregoing we have also T'P'=P'P3 sented by rigidelements which have a common pivot F shiftable along the y-axis. It isfurther possible to introduce a third rigid element of any desiredpredetermined length, for instance GE, which is parallel to the y-axisand vertically movable up and down at a constant distance from thelatter equivalent to OL -=a.GlE.', and with its ends in constantconnection with the two first-named elements. Then it will be necessaryonly to adjust the total cost line. according to the fixed and variablecosts appertaining to any sales volume of a business, whereupon theelement representing the result line will be automatically adjusted inits correct position.

This element GE may also be made useful for measuring the specific yieldand the margin of profit by applying thereto a scale permitting thereading of per cents of its length between the points G and E, forinstance, by dividing that length in 100 equal parts with zero at thepoint Gand 100 at point E. From the foregoing it will be clear that thepoint J of such scale in which the horizontal through E intersects theline GEdirectly indicates the specific yield of a business whose diagramcorresponds to that of Fig. 3. Furthermore, the point H being theintersection of the line FT with GE indicates the margin of profit. Ifthe specific yield is negative, then, according to the diagram of Fig. 4

a line may be plotted through F2 and the point W2 whose distance from;P'z equals A2P'2. The intersection H2 of that line with theaforementioned third element, now in the position GzEz will indicate thenegative specific yield. If the margin of profit is negative as, forinstance, in case of the turnover OT in Fig. 3,, a line may be plottedthrough F and a point P2 which is so defined that its distance from Pequals T'P'. Then, the reading of point H is the negative margin ofprofit.

The determinant may either be found with the aid of the slide Z of Fig.1, or preferably according to another principle. The determinant hasbeen defined as the ratio of the sales in excess of the break-evenvolume over total sales. Thus, the determinant for the sales volume TinFig. 3 is the ratio A horizontal line is plotted through H whichintersects the result line in K. Now, we have the equation ems OT' LThis follows from PT QI T A HJ -and FJ=OL. Consequently, if QL isprovided with a scale divided in 100 equal parts similar to GE and withzero at point L and 100" at point 0, the determinant can be read bycomparison of the length KH with such per cent scale. This method isapplicable for a positive determinant.

If the determinant is negative, for instance, the determinant for asales volume OT, the line Y!" may be plotted. Then a horizontal scalehaving equal increments may be so positioned that the ends of the firstunit length of the scale are positioned on the y-axis and the line F1"respectively. In the example of Fig. 3, it is as sumed that the unitlength of such scale is QR. The scale thus positioned intersects theresult line in point S. If, then, 1 is subtracted from the reading ofthe scale at S, the result will be the negative determinant for theturnover OT owing to EZJ OT QR However, another consideration leads toan even simpler method of establishing the value of the determinant ifthe latter is within the limits of +1 and 1. g The negative determinantbetween these limits can be found in a manner similar to that explainedwith respect to the positive determinant. This is shown in Fig. 5.According to the foregoing, the negative determinant for the salesvolume T in Fig. 5 is If now a point Q on GJ is so selected that HQ'=GHand then a parallel to OL is plotted through Q which intersects FH in S,then is equal to Hence, the negative determinant can be measured withthe same means as the positive, that is to say, with a scale of thelength 0L whose zero mark is at the end corresponding to L and whose 100mark is on the end corresponding to O. The correctness of this statementcan be the aid of the mentioned scale is the negative determinant.

In many instances, however, it is more convenient to apply a scale whosezero point coincides with the y-axis rather than with GJ. This is alsopossible. According to its definition, the positive determinant of thesales volume T in Fig. 3 is 1: OT Considering that 22" 0B FJ ashereinbefore disclosed, the following method may be applied: Make FH=GHand plot I-IK' parallel to CL, then H"K' will be a measure for thedeterminant which may be read on a scale having its zero point on thegr-axis and its mark on the line GJ. Similarly, with reference to Fig.5, the negative determinant of the sales volume T can be read as thelength Q"S" wherein FQ" is equal to GH and the parallel to OL is plottedthrough Q".

Figs. 6 to 15 illustrate the preferred form of an instrument accordingto the present invention and which embodies the features mentioned inthe foregoing disclosure of the principle on which its structure isbased. The instrument comprises a frame in general denoted withthenumeral 20 and being composed of an upper bar 2|, a lower bar 22, twoSide bars 23 and 24 respectively, and an intermediate bar 25 parallel tobar 23. The bars 2|, 22, 23 and 24 are jointed at their corners asindicated at 26 for the lower lefthand corner of the frame, and the bar25 is secured in its position to bars 2| and 22 by means of jointingpieces 21 and 28 respectively. Hinges 29 and 30 are secured to the framebars or members 2| and 22 respectively on the one hand and attached to abase board 3| on the other hand. The hinge axis 32 is arranged at ashort distance from the outer edge of the bar 23 in order to facilitatethe insertion of a sheet of drawing paper if such is to be used, only asmall portion of such paper being shown at 33. Furthermore, adjustmentdevices 29 and 30 may be interpositioned between the board and thehinges proper. By manipulating the thumbscrews of these devicesinaccuracies in the relative position of the frame and board 3| or thesheet 33 on'said board may be corrected. At suitable points, e. g., at34, an upright post 35 may be secured to the board 3| as shown in Fig, 8and project through a corresponding hole 36 when the frame is turneddown on the base. The posts 35 serve to secure the paper sheet 33 incorrect position relatively to the frame by passing throughcorresponding perforations 3'! of the paper. For reasons to be explainedhereinafter, the bars 2| and 22 are set off at the bottom between 38 and39 and between accuse 4D and 4| respectively so as to leave a gap 52between the bottom of the respective frame member and the board 3| asclearly shown in Fig. '7. In order to combine strength with low weightthe individual frame members of the illustrated embodiment consist ofsquare tubes. However, it will be understood that any other suitablecrosssection may be applied with satisfying result.

The bars 23 and 25 are provided with means or are so shaped as toconstitut parallel guide rails for other parts of the instrumentdescribed hereinaften For this purpose, strips 43 and 44 having exactlyparallel edges are secured to the tops of the bars 23 and 25respectively as indicated at 45 and 48 in Figs. 10 and 11. The strips 43and 44 project laterally from the associated bars.

On bar 23, a slide 41 is mounted so as to be shiftable along the bar. Inthe illustrated embodiment, the slide comprises a channel piece 48having inner flank pieces 49 and 58 secured thereto, for instance, byscrews 5| as clearly shown in Figs. 9 and 10. The flank pieces engagewith their upper edges the bottom surfaces of the projecting strips, anda. spring 52 is inserted between the strip 43 and the inner face of thechannel 48 so as to insure parallel guidance of the slide along bar 23and strip 43. An angular piece 53 is secured with one of its legs to theoutside of one of the flanges of the channel 48 as indicated at 54, anda pivot piece 55 is secured to the other leg of the piece 53. The pivotpiece 55 has a semi-circular, annular groove 55 in its bottom surface,and a semi-circular recess 58' of its outer edge 51.

of the recess 56 is located on a line coinciding with the edge 51, Thecenter 58 moving parallel to the bar 23 when the slide 41 is shiftedalong the latter is determinative of the y-axis of the coordinate systemin relation to which members of the instrument are intended to beadjusted. Aline 59 indicating the path of the center 58 and thus they-axis may be provided on the board 3|. Similarly, the paper sheet 33,preferably a squared graph paper, may be provided with a line 59'coinciding with line 59 when the paper sheet is inserted in its positionpredetermined by the posts 35 and perforations 31 shown in Fig. 8.

A plurality of rulers, at least two, are provided I which are pivotedabout the center 58. One of the rulers, denoted by '86, is the "resultruler whose edge 6| is indicative of the afore-mentioned result line,and another one 62 is destined to represent with its edge 63' theafore-mentioned 1 total cost line. Each ruler has a ring-shaped end 64and 64 respectively of approximately threequarters of a circle and soshaped as to fit into the groove 56 of the slide.41. In continuation ofthe ruling edges 6| and 63, the rulers may have narrow tongues 66 and 61respectively which extend from their annular portions inwardly at leastas far as the center 56. Through the remaining clearance 68 marks on thesheet of pa,

per 33 or on the board 3| may be observed when the slide is to beadjusted so that the center 58 through which the ruling edges 61 and 62pass coincides with a selected one of such marks. Although instead ofthe particular type of pivot hereinbefore described any other suitableand conventional type may be used, we prefer the illustrated typebecause it permits the drawing of a line at least along one of the saidedges uninterruptedly to the center point 58, and even beyond thatpoint. In addition to the rulers 5| The arrangement is such that thecommon center 58 of the groove 56 and zontal ruler 10 may be rigidlysecured to the slide 41 so as to establish a parallel to the m-axis ofthe system, which axis may be indicated by a.

line 1| on the board and/or the paper sheet 33. The horizontal ruler 18may be made in one piece with a bottom cover plate 12 screwed to thebottom of pivot piece 55 at 13, after the rulers 69, and 62 have beenplaced in the annular groove 56'. All the rulers should be of relativelyvery thin material, preferably steel or other, metal,

so that even the top ones are as close to the underlying surface of theboard 3| or paper 33 as possible. Now, it will be clear that if theslide 41 is moved up or down the bar 23 the pivot at 58 with all thementioned rulers attached thereto will be shiftedalong the y-axis of thesystem,

and the rulers 88, 62 and 68 can be turned about that pivot an angle ofa size depending on the shape of the clearance 68 and'other parts of theassembly. In other words, the required movability of the rulers can beeasily obtained by correct dimensioning of the cooperating parts.

Means may be provided whereby the members 50 and 62 with respect totheir edges 6| and 63 are so held angularly spaced from each other thanthe equation tan a-i-tan 5:2 discussed hereinbefore in connection withFig. 3 will be fulfilled. In other words, means are provided whereby ata predetermined distance from the y-axis, the spacing of the lines 6|and 63 is maintained constant. This is accomplished in the illustratedembodiment in the following manner:

On bar 25 with strip 44, a carriage is shiftably mounted which comprisestwo slides 8| and 82 in tandem arrangement. Each of the two slidescomprises, similar to the slide 41, a channel piece 83 with inner flankpieces 84 and 85 and a spring 86 as clearly shown in Fig. 12. An

. angular piece 8'! is riveted at 88 with its upright leg to the channel83. The other leg recessed atv der portion 9|) and a narrower portion9|.t The wider portion is provided with a hole 92 whose centerconstitutes a pivot axis denoted by 93 in slide 8| and by 94 in slide82. A pivot piece 95 having a restricted head 96 is passed through thehole 92 as more clearly shown in Fig. 13 and is held in position withrespect 1 to the leg portion by means of a headed screw 91 with washer98. The structure of th pivot at 93 is similar to that at 94. The lowersurface of the piece is provided with a groove 99,

whose one flank passes-diametrically through the i pertaining pivot axis93 or 94; and which has a width; equal to that of the rulers 60 and 62.Ruler '66 is slidably fitted into the groove 99 of'the slide 8| andruler 62 is slidably fitted into that of slide 82 so that the ruleredges 6| and 82 engage the pertaining groove flank which passes throughthe pivot axis of the respective pivot piece 95. Means may be providedto prevent the rulers from dropping out of their pivot pieces. at leastone of the groove flanks, e. g. 100, may be dove-tailed and thecorresponding edges of the rulers may be beveled over that length which.

may come into engagement with the pivot pieces.

For this purpose,

The two narrower portions 9I of the two slides BI and 82 are rigidlyconnected to each other by a fiat piece IIII riveted or otherwisesecured thereto as indicated at I02. Piece IDI has a straight edge I93parallel to the y-axis and in line with the two pivot centers 93 and 94.This edge I03 is provided with a percentage scale I04, meaning that thetotal distance between the points 93 and 94 is divided in preferably onehundred equal parts with the zero mark at 93 and 100 mark at 94.. Now;it will be clear that if the carriage 80 is shifted along bar whileslide 41 is held in any desired position in relation to frame bar 23,the rulers fill and 62 will be swung about the slide pivot 58 and willsimulta-- neously slide in the grooves 99 and, thus, turn the pivotpieces 95. In other words, at a predetermined horizontal distance fromthe pivot point 58, the rulers are spaced a predetermined distancedefined by the distance of the pivot axes 93 and 94 from each other. Inorder to permit an adjustment of the various members within sufiicientlywide limits the rulers 99 and 62 are of such a length that they protrudeinto the space between the frame bars 25 and 24. Similarly, the rulers69 and III may extend beyond the bar 25. To allow this, frame bar 25 isspaced from the top surface of the board 3| as clearly shown at I05 inFig. 12, and the rulers are passed underneath the bar 25. For a similarreason, the aforementioned recesses 42 are provided between two points38 and 39 on bar H and between points 49 and 4| on bar 22.

From the above-discussion of the diagram of Fig. 3 it will be apparentthat the distance of the pivots .93 and 94 from each other may be freelyselected. However, the ratio of the distance of point 58 from the edgeI03 over the distance from 93 to 94 is determinative of the value 2, i.e., of the ratio of the increment of a scale to be applied to the x-axisover the increment of a scale to be applied to the y-axis. Reversely, ifthe said increments are pre-selected the ratio of the mentioneddistances must be equal to the ratio of the increments. In mostinstances, it will be preferred to apply equal increments to both the:cand y-axes of the system whereby the value 2 is equal to 1. In thatevent, the distance from point 58 to the line 93-94 must be equal to thedistance 93 to 94. This is shown in the illustrated embodiment. However,it is to be understood according to the foregoing that the two distancesmay differ from each other in'which case it is only necessary. to selectthe ratio of the co-ordinate increments accordingly. Furthermore, itwill be understood that in no event is it required that the incrementsof the scale I04 be equal to those of the y-axis. On the contrary, incertain cases it may be most convenient to use for the co-ordinate axesincrements different from those of the scale I04 which as stated aboveis preferably a percentage scale having an increment equal toone-hundredth of the distance from 93 to 94.

Portions of the afore-mentioned scales of the :cand y-axes are indicatedat H0 and III respectively as applied to the board. If a paper sheet 33is used it is advisable to have them printed on the latter inorder tofacilitate the application of the instrument. Furthermore, a scale H2similar to that of the :c-axis may be provided on the horizontal rulerH2. For many purposes of use. it is advisable to provide a shiftablevertical ruler and a shiftable horizontal ruler in addition to therulers hereinbefore described. Since, however, these additional rulersare not always needed it is preferred to mount them detachably onsuitable frame members. In the illustrated embodiment such verticalruler H3 is secured to two channel-shaped slides H4 guided along theflanks of the bars 2I and 22 respectively. Thus, the ruler H3 may beeasily put on and removed from the instrument as the user may desire. A.scale H3 may be applied to the ruler having its zero point coincidingwith the .r-axis and counting upward and downward as the scale of they-axis. An additional slide H5 shiftable along the vertical ruler H3 maybe provided. Such slide with percentage scale H6 on one or either sidehas been more fully described in the afore-mentioned application, SerialNo. 356,432 filed September 12, 1940. The additional horizontal rulerIII is secured to a slide H8 which may consist of a channel interiorlyrecessed at H9 as shown in Fig. 15 so as to embrace the guide strip 43of the bar 23. In order to permit the slide to be brought into operativeposition, the strip 43 may .end at a sufficient distance from the bars2| and 22. Then the slide H8 can first be placed on one of the ends ofthe bar 23 which are not covered by the strip 43 and, then, shiftedalong that bar so that the stripwill engage the recesses H9. The freeend of the ruler H1 is passed underneath the bar 25. In accordance withcertain purposes of ruler-H1 a percentage scale I20 may be appliedthereto having its zero mark co-incident with the y-axis and its flOOmark at a distance therefrom equal to the distance of point 58 from theedge I03. Another scale I2I may be also provided on ruler I II, whoseincrements are equal to those of the zraxis.

Now, in using the instrument according to the present invention, eitherthe location of the xaxis may be considered as stationary and the pivotpoint 58 movable in relation thereto in order to adjust the distance Iof the diagrams Figs. 1 and 3, or the :c-axis may be movable in relationto the point 58 while the latter is in a fixed position. In the case ofthe first alternative line II or an equivalent line on the paper sheet33 is useful as :r-axis in relation to which the point 58 may beadjusted by shifting the slide 41 along the bar 23. In the other case,the slide 41 may be held or made stationary in relation to the bar 23and the adjustable x-axis may be represented by the edge of theshiftable ruler HIor by a line on the board 3I or graph paper 33 at thedesired distance from 58 and selected from a plurality of parallel linessuch as shown at II and II. However, the first alternative is preferablebecause it does not require, as in the second case, a change of the zeropoint of the system from which the scale of the y-axis must count. Inother respects, there are no essential differences between the mentionedalternatives. For this reason, only the first one will be describedhereinafter.

If a graph paper 33 is to be used, the frame 20 is swung open, i. e.away from the board 3I, about the hinges 29 and 39. The paper sheet isplaced on the board with its perforations 37 in engagement with the pinsor posts 35, and the frame is turned on top of the paper sheet, wherebythe latter is held in its correct position without substantial strain atthe perforations. Then slide 41 is shifted to the desired distance ofthe point 58 from the m-axis, i. e. line I I, according to the fixedcosts of the business under consideration. Thereafter, ruler 62 is to beso turned about Divot 5| that its edge 63 passes through a point whoseabscissa :c equals the contemplated sales volume, and whose ordinate -yequals the total costs incidental with the sales volume in the measureof the scales of the axes. The pertaining point (:r, y) may be easilydetermined either with the aid of the net of the graph paper or with theaid of the vertical ruler H3 shifted with its edge to the respectivepoint a: on the x-axis. Adjustment of the ruler 62 eifects also theadjustment of the ruler 60 by the intermediary of the carriage 80 withits accessorial parts. This completes the diagrams of Figs. 1 and 3 asfar as the lines OT,

FA, FW, FF and PW in Fig. 1 and the lines OL, FJ, FE, GE and PW in Fig.3 are concerned. The

break-even point is determined by the intersec-' tion of the ruler edge6| with the line H. The variable and total costs and the profit or lossfor any other sales volume may be directly read as the lengths of theordinate of a selected abscissa between edge 62 and 10, between 62 andthe m-axis, and between the .r-axis and the edge Bl respectively. If sodesired, additional rulers of the type of ruler 69 may be so adjustedbetween rulers 10 and 62 as to divide the variable costs into selectedgroups.

The specific yield is directly readable on the scale I04 as theintersection of the top edge of ruler 10 with the edge I03. On the samescale the margin of profit is readable as the point of intersection ofedge I03 with the upper edge of ruler 69 when the latter is so turnedthat its upper edge passes through that point on the line H whichcorresponds to the sales volume in consideration. In order to find thedeterminant the ruler 69 remains in the last-mentioned position. Rulerill is to be shifted to a position where the distance of its upper edgeupwards from that of ruler 10 is equal to the distance of point 93 fromthe point of intersection of edge )3 with the edge of ruler 69. Then,the determinant may be read on scale i at the intersection of the rulers69 and I H.

not above mentioned may also be solved with the described instrument. Ofsuch problem only a specific one which has been found particularlyimportant will be discussed hereinafter in reference to Fig. 16. Inconnection with the diagrams of Figs. 1 and 3, it is frequentlydesirable to plot the so-called cost reduction curves which show how thelocation of the break-even point on the :c-axis changes, when, for agiven sale volume, savings in fixed and/or variable costs can be made.This is illustrated in Fig? 16 where it is assumed that a certainbusiness to be analyzed turned out a sales volume s at total costs ofj+v wherein f is the fixed costs and v the variable costs. Consequently,and according to the above explanation, the slide 41 of Fig. 6 has beenso shifted in Fig. 16 that the pivot 58 coincides with point-F of thediagram which, in the scale measure of the system, is spaced from thezero point 0 a distance equal to the quantity 1. Point T is sodetermined on the :c-axis that its distance from 0 equals the quantitys. Finally, ruler 62 has been so turned that its edge 63 passes throughW From the foregoing description it will be clear that the instrumentpermits the finding of certain data essential in the management of abusiness if the fixed and variable costs incidental to a given salesvolume are known. However, and this is a highly important feature, it isalso possible with the aid of the instrumentto find those conditionswhich must prevail in order that a desired result be obtained. If, e. g.it is intended to reach a predetermined specific yield when there arefixed costs of a given amount, it will be necessary only to shift point58 to the corresponding distance from O, and the scale H14 so that theruler l0 intersects that scale in the point corresponding to the desiredyield. Then, the co-ordinate values of sales volume, variable cost,profit and break-even point are immediately readable from the positionof the various'rulers in relation to each other. Similar readings as tothe different factors may be obtained if the margin of profit or thedeterminant is one of the predetermined quantities.

It will be unnecessary to describe further in de'-- tail themanipulation of the difierent members of the instrument and among themthe slide H6 which corresponds to the slide Z in Figs. 1 and 2 insolving the various problems discussed in connection with the diagram ofFigs. 1 to 5. It sufilces to say that these problems may be solved withthe disclosed mean in a particularly easy manner without the requirementof making many elaborate and cumbersome calculations heretoforenecessary in the analysis and management of business enterprises. Agreat variety of problems located on the ordinate of Tin the .r, yquadrant and spaced from T a distance according to f+v. Owing to theconnection of the rulers 60 and 62 by means of carriage 80 in Fig. 6,the ruler edge 6! will then automatically take the position FG, where itintersects the x-axis in the break-even point B. The diagram shows thatthere is a loss corresponding to TP for the sales volume OT. Therefore,the management of the business enterprise will try to shift thebreak-even point towards the left in order to change the loss into aprofit. This might be done by a reduction of the fixed costs. Now, thediagram directly shows without the requirement of any additional line orcurve what reductions are required to shift the breakeven point to adesired position; or reversely, what the location of the new break-evenpoint will be a given amountikt length ofthe abscissa RmRu is also thatof the I new break-even point B10.

In order to plot the cost reduction curve for the variable costs when nochange in the fixed costs takes place, the following method isrecommended: Assume the saving in a case under consideration to be equalto UmW, then turn edge 65 so as to coincide with point U10 on the lineT'W whereupon the edge- M will intersect the :r-axis in the newbreak-even point Bu. If, now, the point C11 is determined whose ordinate011311. is equal to WU10 and whose abscissa U11Ci1 is equal to that ofthe new break-even point B11, then point C11 is a point of the desiredcurve Zn, By applying the same method to other values of savings, morepoints may be determined through which the curve Z0 can be plotted.

variations of the shift the break-even point A series of curves may beplotted each of which shows the shifting of the break-even point as theresult of savings in variable costs if simultaneously a predeterminedsaving in the fixed costs takes place. Such a curve is also shown inFig. 16 and denoted by Z1. This curve is found in the following manner:First, the point F is shifted to F12 according to the saving in fixedcosts for which the curve Z1 is to be plotted. This shifting should takeplace in such a manner that edges 63 and 6| remain parallel to theirrespective original positions. Their new location is I63 and IGIrespectively; I63 intersects line 'I'W in the point Wu, and INintersects the x-axis in point B12. From then on, the procedure issimilar to that described with reference to curve Z0. Edge I83 is turnedabout F12 into the position 263 where it intersects the line TW in thepoint U12 spaced from W12 a distance corresponding to a contemplatedsaving in variable, costs. turning of line l63 simultaneously causesturn- Thising of 161 into the position 26! defining the new The desiredpoint of the C13 whose abscissa break-even point B13. curve Z1 is, then,point U13C1a is equal to 0313 and whose ordinate C13B13 is equal toU12Wi2.- Hence, any point C13 of the curve Z1 indicates ,that thebreak-even point B1: having the same abscissa length as C13 can beobtained for a sales volume T if the fixed costs can be reduced anamountcorresponding to FFiz and the variable costs an amount corresponding to0131313. In a similar manner additional curves of the type Z1 may beplotted which will permit judicial selection of the most appropriatemeasures in order to improve the business enterprise underconsideration.

It will be apparent to those skilled in the art that many alterationsand modifications of the instrument hereinbefore described are withinthe scope ofthe present invention which is defined by the appendedclaims.

We claim:

1. An instrument for analyzing a business enterprise comprising meansdeterminative of the two axes of a rectangular co-ordinate system, amember embodying a pivot perpendicular to the plane of the two axes ofthe system and movable along the first one of said system axes, two81.91 ments mounted on said pivot and being determinative each of astraight line intersecting the pivot axis, one of said elements beingangularly adjustable in the quadrant between said first system axis andthe one side of a line through the pivot axis and parallel to the secondsystem axis, and the other element being angularly adjustable in thequadrant between the first system axis and the other side of saidparallel.

2. An instrument for analyzing a business enterprise comprising a firstmeans of the positive leg and the negative leg of the first one of thetwo axes of a co-ordinate system, second means determinative of thepositive leg of the second axis of said system, third means embodying apivot whose axis .intersects said first system axis at right angles tothe plane of thetwo axes 0t said system, one of said second and thirdmeans being variable as to its distance from the other one,'and twoelements mounted on said pivot and straight line intersecting said pivotaxis, one of said elements being angularly adjustable in the quadrantbetween the first system axis and the one side of a parallel to saidsecond system axis through said pivot axis, and the second element beingangularly adjustable in the quadrant bebeing determinative each of a.

determinative distance from the said second system axis,

tween the first system axis and the other side of said parallel.

3. An instrument for analyzing a business enterprise comprising a firstmember determinative of the positive leg and the negative leg of thefirst one of the two axes of a co-ordinate system, a second memberdeterminative of the positive leg of the second axis of said system, athird member embodying a pivot whose axis intersects said first systemaxis at right angles to the plane of the two axes of said system, saidthird member being adjustable as to its distance from said second systemaxis, and two elements mounted on said pivot and being determinativeeach of a straight line intersecting said pivot axis, one of saidelements being angularly adjustable in the quadrant between the firstsystem axis and the one side of a parallel to said second system 1 axisthrough said pivot axis, and the second element being angularlyadjustable in the quadrant between the first system axis and the otherside of said parallel.

4. An instrument for analyzing a business enterprise comprising a firstmember determinative of the positive leg and the negative leg oi thefirst one of the two axes of a co-ordinate system, a second memberdeterminative of the positive leg of the second axis of said system, athird member embodying a pivot whose axis intersects said first systemaxis at right anglcs to the plane of the two axes of said system, saidsecond member being movable along said first system axis and adjustableas to its distance from said third member, and two elements mounted onsaid pivot and being determinative each of a straight line intersectingsaid pivot axis, one of said elements being angularly adjustable in thequadrant between the first system axis and the one side of a parallel tosaid second system axis through said pivot axis, and the second elementbeing angularly adjustable in the quadrant between the first system axisand the other side of said parallel.

5. An instrument for analyzing a business enterprise comprising a firstmember determinative of the positive leg and the negative leg of thefirst one or the two axes of a co-ordinate system. a second memberdeterminative of the positive leg or the second axis of said system andincluding a plurality of lines parallel to said second system axis, athird member embodying a pivot whose axis intersects said first systemaxis at right angles to the plane or the two axes of said system, andtwo elements mounted on said pivot and being determinative each of astraight line intersecting said pivot axis, one of said elements beingangularly adjustable in the quadrant between the first system axis andthe one side of a parallel to said second system axis through said pivotaxis, and the second element being angularly adjustable in the quadrantbetween the first system axis and the other side of said parallel.

6. An instrument for analyzing a business enterprise comprising meansdeterminative of the positive and the negative leg of the first axis,and of the positive leg of the second axis of a co-ordinate system, amember embodying a pivot 'whose axis'irrtersects said first system axisat right angles to'the plane of the two axes of said system, said memberbeing adjustable as to its at least'three elements mounted on said pivotand being determinative each of a straight line radial with respect tosaid pivot axis, one of said elements being angularly adjustable in thequadrant between the first system axis and the side of a parallel tosaid through said pivot axis,

angularly adjustable in the q first system axis and the other side 01'said par-' element being angularly movallel, and the third able in bothsaid quadrants.

one second system axis the second element being uadrant between the 7.An instrument as claimed in claim 6 further comprising a ruler securedto said member and having an edge parallel to axis and radial withrespect 8. In an instrument of the structural triangle including a saidsecond system 10 to said pivot axis. type described, a pivot whose axisconstitutes the apex of said triangle, a first shiftable memberdeterminative predetermined length and c of said triangle, and a second.ber of variable efiective lengths and constituting of a straight lineof 5 onstituting the base and a third memthe sides of said triangle,said second and third members being connected to said pivot so as to andmeans for guiding said direction of said straight line. 9. In aninstrument of the first member in the type described, the

combination of means determinative-of an axis of a co-ordinate system,with ing its axis perpendicular t system and intersecting said systemaxis, two elea first pivot hav- 0 the plane of said ments rotatablymounted on said first pivot and being determinative each of a withrespect to said pivot ax from said pivot axis and bei line parallel tosaid system axis, said member straight line radial is, a member spacedng shiftable along a including a second and third pivot having theiraxes spaced a predetermined distance from each other and intersectingsaid last-mentioned line,

said two elements being in shiftable engagement with said second andthird pivot respectively so that the lines determined by sect therespective pivot axes.

10. A devic as claimedin first pivot comprises a memb said elementsinterclaim 9 wherein said r having a side face and a substantially fiatbottom surface, said side face being provided with and said bottomsurface semi-circular recess having a semi-circular annular groove withan inner diameter larger than that of cess and of said groov coinc axis,and wherein each of sai said recess, the centers of said reiding withsaid pivot (1 elements is formed by a relatively thin and narrow rulerhaving one end shaped as a ring sector of substantially three-.

quarters of a circle, the w-id said sectors corresponding to th anddiameters of those of said groove,

and each of said elements including a ruling edge extending tongue-likeat least as far as th center of said recess, when sa sectors into saidgroove of the sorted with said pivot member.

11. A device as claimed in id elements are in-- claim 9 wherein saidmember and said second and third pivots comprise an elongated bodyembodying near its ends,

bearings with vertical axes, a disc-like piece with a restricted headjournaled in each of said bear- (:5

ings, the'bottom face of each disc -like face bein provided with agroove having parallel flanks one of which being diametrical axis of therespective bearing,

with respect to the th width of said groove corresponding to that of oneof said elements, and means to prevent said element from dropping out ofsaid groove when in engagement therewith.

combination of a first and a s econd guiding means allel guides, and theaxes of said third pivot intersecting a line parallel to said secondguiding means and be mounted on said pivot and being determinative eachof a line radial with respect to the pivot axis,

slide or a turning ments about said pivot.

14. An instrument for analyzing a business enterprise comprising meansof said eleaxis and spaced therefrom a predetermined distance, a secondslide movable along said second guiding means and including a second anda third pivot spaced from each other a predetermined distance and havingaxes perpendicularly intersecting a line parallel to the first systemaxis-said elements being connected to said second and third pivotsrespectively for rotation and being lengthwise shiftable thereto, apercentage scale on said second slide and having its two and markscoinciding with the axes of said second and said third pivotrespectively, and a third element rotatably mounted on said first pivotand being determinativ of a straightvline radial with respect to theaxis of said first pivot whereby said line determined bysaid thirdelement is useful as an indicator in relation to said percentage scale;

15. An instrument as claimed in claim 14 further comprising a rulerparallel to said second system axis and co-ordinate system, a slideincluding a pivot having its axis perpendicular to the plane 01 saidsystem, first means for guiding said slide with said pivot axis alongsaid first system axis, two elements mounted on said pivot and beingdeterminative each of a line radial with respect to the pivot axis,second guiding means parallel to said first system axis and spacedtherefrom a predetermined distance, a second slide movable along saidsecond guiding means and including a second and a third pivot spacedfrom each other a predetermined distance and having axes perpendicularlyintersecting a line parallel to the first system axis, said elementsbeing connected to said second and third pivots respectively forrotation and being lengthwise shiftable thereto, a percentage scale onsaid second slide and having its two end marks coinciding with the axesof said second and said thirdpivot respectively, and a third elementrigidly connected to said first slide and being determinative of astraight line parallel to said second axis and radial with respect tothe axis of said first pivot whereby said line determined by said thirdelement is useful as an indicator in relation to said percentage scale.

17. An instrument for analyzing a business enterprise, comprising meansdeterminative of the position and the negative leg of the first axis,and of the positive leg of the second axis of a co-ordinate system, aslide including a pivot having its axis perpendicular to the plane ofsaid system, first means for guiding said slide with said pivot axisalong said first system, a first, a second, and a plurality of thirdelements mounted on said pivot and being determinative each of astraight line radial with respect to the pivot axis, second guidingmeans parallel to said first system axis and spaced therefrom apredetermined distance, a second slide movable along said second guidingmeans and including a second and a third pivot spaced from each other apredetermined distance and having axes perpendicularly intersecting aline parallel to the first system axis, said first and said secondelement being connected to said second and third pivots respectively forrotation and being lengthwise shiftable thereto, a percentage scale onsaid second slide and having its two end marks coinciding with the axesof said'second and said third pivot respectively, whereby the linedetermined by at least one of said third elements is useful as anindicator in relation to said percentage scale.

18. An instrument comprising a base board, a frame hinged to said board,means in connection with said board and determinative of at least one ofthe axes of a co-ordinate system, with the said frame including a firstguiding member parallel to said axis and a second guiding means parallelto and spaced from said first guiding means, a first slide shiftablealong said first guiding means and including means determinative of afirst variable point on said system axis, a second slide shiftable alongsaid second guiding means and including means determinative of a secondand a third variable point, said second and said third point beingspaced from each other a predetermined distance and being located on aline parallel to said system axis, a first and a second elementconnected to' said first and to said second slide, said first elementbeing indicative of a straight line between said first and said secondpoint, and said second element being indicative of a straight linebetween said first and said third point, and a third element inconnection with the first slide for indicating the height of thetriangle whose apex is constituted by said first point and whose base isconstituted by the line connecting said second and third point.

19. An instrument for analyzing a business enterprise comprising meansdeterminative oi the positive and the negative leg of the first axis andof the positive leg of the second axis of a co-ordinate system, scalesin connection with said axes respectively, a structural trianglevariable as to its angles and as to its position relatively-to saidaxes, said triangle including a member determinative of the triangleapex and being shiitable along said first system axis, and a memberdeterminative of the triangle base having a predetermined length, andbeing parallel to said first system axis and lengthwise shiftable, andmeans for maintaining a predetermined spacing of said apex from saidbase, the ratio of the increment of the scale of said first axis overthe increment of the scale of the second axis being equal to the ratioof thelength of said triangle base over the distance of said apex fromsaid base.

20. An instrument as claimed in claim 19 wherein the increments of saidscales are equal to each other and the lengths of the base and of theheight of the triangle are also equal.

HERBERT WALLER. ALFRED F. SCHLOMANN.

